"I know her."

Translation: Jag känner henne.

[Newton7]

Does Jag vet henne mean something else?

[Lundgren8]

Vet is only used for knowing facts, not people.

[HoroTanuki]

But if you acidentally say "Jag vet henne" once, would native speakers understand what you meant or?

[Tehed]

Not sure, if anyone will be able to answer that, but...

Is the difference between "vet" and "känner" the same as between "wissen" and "kennen" in German?

[Zmrzlina]

My knowledge of German is limited, but if wissen is for knowledge and kennen is for people and feelings, yes.

[Tehed]

Well... that is basically the explanation, we Germans give to German-learners :D
So it seems the meaning of those words is pretty much the same as their German counterparts.

Thanks a lot!

[Nierls]

so it's the same for Dutch vet = weten, kännen = kennen?

[Zmrzlina]

Yes, that's the feeling I've gotten from studying Dutch here on Duolingo. :)

[IoannisTas1]

For anyone who speaks French, the difference between vet vs känner is the same as savoir vs connaître. Or if you speak portuguese, saber vs conhecer.